The 32-year-old fireman has a clause in his contract which allows him to make the switch to the English division.
Griffith's scored Argyle's only goal in a recent pre-season win over Truro before returning to Wales for work.
"I don't have an awful lot of time left and this would be a great way to end," he told BBC Sport.
"They have to go away and come up with some sort of contract and I have to go to my employees, the Fire Service, and ask if it's okay to have a career-break.
"Without that, it's not something I would really consider. I certainly want to return to my job if I do get the opportunity to go down to Plymouth. But I would like to play in the Football League before my career comes to an end."